The Resource Optimal Transportation Networks : Models and Theory, by Marc Bernot, Vicent Caselles, Jean-Michel Morel, (electronic resource)

Optimal Transportation Networks : Models and Theory, by Marc Bernot, Vicent Caselles, Jean-Michel Morel, (electronic resource)

Label
Optimal Transportation Networks : Models and Theory
Title
Optimal Transportation Networks
Title remainder
Models and Theory
Statement of responsibility
by Marc Bernot, Vicent Caselles, Jean-Michel Morel
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume
Member of
Is Subseries of
http://library.link/vocab/creatorName
Bernot, Marc
Dewey number
515.64
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • U8cMKzmAHqo
  • zrtN7BEVXTE
  • ygBAN815i4w
Image bit depth
0
Language note
English
LC call number
  • QA315-316
  • QA402.3
  • QA402.5-QA402.6
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Caselles, Vicent.
  • Morel, Jean-Michel.
Series statement
Lecture Notes in Mathematics,
Series volume
1955
http://library.link/vocab/subjectName
  • Mathematical optimization
  • Engineering economy
  • Operations research
  • Mathematics
  • Calculus of Variations and Optimal Control; Optimization
  • Operations Research, Management Science
  • Engineering Economics, Organization, Logistics, Marketing
  • Operations Research/Decision Theory
  • Applications of Mathematics
Label
Optimal Transportation Networks : Models and Theory, by Marc Bernot, Vicent Caselles, Jean-Michel Morel, (electronic resource)
Instantiates
Publication
Note
ISSN 0075-8434 for print edition
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Introduction: The Models -- The Mathematical Models -- Traffic Plans -- The Structure of Optimal Traffic Plans -- Operations on Traffic Plans -- Traffic Plans and Distances between Measures -- The Tree Structure of Optimal Traffic Plans and their Approximation -- Interior and Boundary Regularity -- The Equivalence of Various Models -- Irrigability and Dimension -- The Landscape of an Optimal Pattern -- The Gilbert-Steiner Problem -- Dirac to Lebesgue Segment: A Case Study -- Application: Embedded Irrigation Networks -- Open Problems
Dimensions
unknown
Edition
1st ed. 2009.
Extent
1 online resource (X, 200 p. 58 illus., 5 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783540693154
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-540-69315-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000546316
  • (SSID)ssj0000447013
  • (PQKBManifestationID)11314939
  • (PQKBTitleCode)TC0000447013
  • (PQKBWorkID)10505016
  • (PQKB)10797610
  • (DE-He213)978-3-540-69315-4
  • (MiAaPQ)EBC3063516
  • (EXLCZ)991000000000546316
Label
Optimal Transportation Networks : Models and Theory, by Marc Bernot, Vicent Caselles, Jean-Michel Morel, (electronic resource)
Publication
Note
ISSN 0075-8434 for print edition
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Introduction: The Models -- The Mathematical Models -- Traffic Plans -- The Structure of Optimal Traffic Plans -- Operations on Traffic Plans -- Traffic Plans and Distances between Measures -- The Tree Structure of Optimal Traffic Plans and their Approximation -- Interior and Boundary Regularity -- The Equivalence of Various Models -- Irrigability and Dimension -- The Landscape of an Optimal Pattern -- The Gilbert-Steiner Problem -- Dirac to Lebesgue Segment: A Case Study -- Application: Embedded Irrigation Networks -- Open Problems
Dimensions
unknown
Edition
1st ed. 2009.
Extent
1 online resource (X, 200 p. 58 illus., 5 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783540693154
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-540-69315-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000546316
  • (SSID)ssj0000447013
  • (PQKBManifestationID)11314939
  • (PQKBTitleCode)TC0000447013
  • (PQKBWorkID)10505016
  • (PQKB)10797610
  • (DE-He213)978-3-540-69315-4
  • (MiAaPQ)EBC3063516
  • (EXLCZ)991000000000546316

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